few_shots: Example:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K
options: Interpret functions that arise in applications in terms of the context.

Model periodic phenomena with trigonometric functions.

Interpret expressions for functions in terms of the situation they model.

Analyze functions using different representations.

Define, evaluate, and compare functions.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.
problem_activity: Activity
The purpose of this activity is for students to make connections between different representations of functions and start transitioning from input-output diagrams to other representations of functions. Students match input-output diagrams to descriptions and come up with equations for each of those matches. Students then calculate an output given a specific input and determine the independent and dependent variables.
Launch
Arrange students in groups of 2. Give students 3–5 minutes of quiet work time and time to share their responses with their partner and come to agreement on their answers. Follow with whole-class discussion.
Student Facing
Record your answers to these questions in the table provided.
Match each of these descriptions with a diagram:
the circumference,
\(C\)
, of a circle with
radius
,
\(r\)
the distance in miles,
\(d\)
, that you would travel in
\(t\)
hours if you drive at 60 miles per hour
the output when you triple the input and subtract 4
the volume of a cube,
\(v\)
given its edge length,
\(s\)
Write an equation for each description that expresses the output as a function of the input.
Find the output when the input is 5 for each equation.
Name the
independent
and
dependent variables
of each equation.
[IMG]
|              description               | a | b | c | d |
|----------------------------------------|---|---|---|---|
|                diagram                 |   |   |   |   |
|                equation                |   |   |   |   |
| input = 5                   output = ? |   |   |   |   |
| independent                   variable |   |   |   |   |
|  dependent                   variable  |   |   |   |   |
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Choose a 3-digit number as an input.
Apply the following rule to it, one step at a time:
Multiply your number by 7.
Add one to the result.
Multiply the result by 11.
Subtract 5 from the result.
Multiply the result by 13
Subtract 78 from the result to get the output.
Can you describe a simpler way to describe this rule? Why does this work?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
The goal of this discussion is for students to describe the connections they see between the different entries for the 4 descriptions. Display the table for all to see and select different groups to share the answers for a column in the table. As groups share their answers, ask:
“How did you know that this diagram matched with this description?” (We remembered the formula for the circumference of a circle, so we knew description A went with diagram D.)
“Where in the equation do you see the rule that is in the diagram?” (The equation is the dependent variable set equal to the rule describing what happens to the independent variable in the diagram.)
“Explain why you chose those quantities for your independent and dependent variables." (We know the independent variable is the input and the dependent variable is the output, so we matched them up with the input and output shown in the diagram.)
Speaking: MLR8 Discussion Supports.
As students describe the connections they noticed in the table across from the different entries for the four descriptors, revoice student ideas to demonstrate mathematical language use. In addition, press for details in students’ explanations by requesting that students challenge an idea, elaborate on an idea, or give an example. This will help students to produce and make sense of the language needed to communicate their own ideas about functions and independent and dependent variables.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 4